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تسجيل مستخدم جديد$L^2$-torsion invariants and the Magnus representation of the mapping class group
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In this paper, we study a series of $L^2$-torsion invariants from the viewpoint of the mapping class group of a surface. We establish some vanishing theorems for them. Moreover we explicitly calculate the first two invariants and compare them with hyperbolic volumes.
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We calculate the abelianizations of the level $L$ subgroup of the genus $g$ mapping class group and the level $L$ congruence subgroup of the $2g times 2g$ symplectic group for $L$ odd and $g geq 3$.
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